We have scaled Equations (REF ), (REF ), and (REF ) using reasonable values (with \(\dot{M} \)  close to the minimum \(\dot{M} \gtrsim 5\times 10^{-7}~M_{\mathrm {J}}\,\mathrm {yr}^{-1}\)  derived by [1]} for PDS 70 b) but one should remember that the parameter space is large, with especially \(\dot{M} \) , \(M_{\mathrm {p}}\) , and \(f_{\mathrm {fill}}\)  varying by orders of magnitude. Profiles in \(\rho \) –\(T\)  space are shown for a range of parameters in Figure REF . Densities are \(\rho \sim 10^{-16}\) –\(10^{-9}\)  g cm\(^{-3}\)  and temperatures \(T\sim 100\) –\(10^4\)  K, with approximately \(T\propto \rho ^{1/3}\) , as can be seen from Equations (REF ) and (REF ) for \(\zeta \approx 1\) . An extensive discussion of the profiles, in particular against radial distance from the planet, is given in [2]}.
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